You can remove campaigns from showing up in this list by moving them from Active to Drafts (this will also remove them from any Campaign Menu they were added to and make them not available to select in the Integration Center).
Remove the "Check Out Our Other Campaigns" button per campaign
You can also remove this button altogether. To remove the button from your campaign site, go to Campaigns > Edit This Campaign (choose a campaign) > Landing Page Appearance > Footer. Here, you can toggle Other Campaigns Button to "Hide", and it will remove this from your campaign.
Be sure to click Save!
Remove the "Check Out Our Campaigns" Button in Campaign Presets
You can turn off this setting for all future campaigns by going to Campaigns > Campaign Presets > Landing Page. Within this section is a Footer area where you can likewise toggle this button to "Hide".